Question

Simplify

$3\frac{1}{2} + 5\frac{2}{3} - 4\frac{7}{6}$

• A. 8
• B. 12
• C. 4
• D. 2

Answer 1

Answer:

C. 4

The answer is 4.

Step 1: Convert the mixed fractions into improper fractions

* $3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}$

* $5\frac{2}{3} = \frac{(5 \times 3) + 2}{3} = \frac{17}{3}$

* $4\frac{7}{6} = \frac{(4 \times 6) + 7}{6} = \frac{31}{6}$

Step 2: Write the expression with the improper fractions

$\frac{7}{2} + \frac{17}{3} - \frac{31}{6}$

Step 3: Find a common denominator

The lowest common multiple (LCM) of 2, 3, and 6 is 6.

* $\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}$

* $\frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6}$

Step 4: Combine and calculate

$\frac{21 + 34 - 31}{6}$

$\frac{55 - 31}{6} = \frac{24}{6} = \mathbf{4}$